To simplify the expression [tex]\( y^4 \sqrt[4]{y^2} \)[/tex], let's break it down step by step.
1. Identify the components: We have two parts in the given expression:
- [tex]\( y^4 \)[/tex]
- [tex]\( \sqrt[4]{y^2} \)[/tex]
2. Rewrite the fourth root using exponents: Recall that the fourth root of [tex]\( y^2 \)[/tex] can be written as an exponent:
[tex]\[
\sqrt[4]{y^2} = y^{2/4}
\][/tex]
3. Simplify the exponent: Simplify the fraction in the exponent:
[tex]\[
y^{2/4} = y^{1/2}
\][/tex]
4. Combine the exponents: Now multiply the expressions with the same base [tex]\( y \)[/tex]:
[tex]\[
y^4 \cdot y^{1/2}
\][/tex]
5. Add the exponents: When multiplying expressions with the same base, you add the exponents:
[tex]\[
y^4 \cdot y^{1/2} = y^{4 + 1/2}
\][/tex]
6. Simplify the addition in the exponents: Add the exponents:
[tex]\[
4 + \frac{1}{2} = 4 + 0.5 = 4.5
\][/tex]
7. Write the final simplified expression:
[tex]\[
y^{4.5}
\][/tex]
So, the simplified form of [tex]\( y^4 \sqrt[4]{y^2} \)[/tex] is [tex]\( y^{4.5} \)[/tex].
